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Journal Articles Journal of Computational and Applied Mathematics Year : 2022

Polynomial-reproducing spline spaces from fine zonotopal tilings

Abstract

Given a point configuration A, we uncover a connection between polynomialreproducing spline spaces over subsets of conv(A) and fine zonotopal tilings of the zonotope Z(V) associated to the corresponding vector configuration. This link directly generalizes a known result on Delaunay configurations and naturally encompasses, due to its combinatorial character, the case of repeated and affinely dependent points in A. We prove the existence of a general iterative construction process for such spaces. Finally, we turn our attention to regular fine zonotopal tilings, specializing our previous results and exploiting the dual graph of the tiling to propose a set of practical algorithms for the construction and evaluation of the associated spline functions.
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Dates and versions

hal-03505795 , version 1 (03-01-2022)

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Hélène Barucq, Henri Calandra, Julien Diaz, Stefano Frambati. Polynomial-reproducing spline spaces from fine zonotopal tilings. Journal of Computational and Applied Mathematics, 2022, 402, pp.113812. ⟨10.1016/j.cam.2021.113812⟩. ⟨hal-03505795⟩
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